Properties of some ∗-dense-in-itself subsets
ℐ-open sets were introduced and studied by Janković and Hamlett (1990) to generalize the well-known Banach category theorem. Quasi-ℐ-openness was introduced and studied by Abd El-Monsef et al. (2000). These are ∗-dense-in-itself sets of the ideal spaces. In this note, properties of these sets are fu...
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| Format: | Article |
| Language: | English |
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Wiley
2004-01-01
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| Series: | International Journal of Mathematics and Mathematical Sciences |
| Online Access: | http://dx.doi.org/10.1155/S0161171204403391 |
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| author | V. Renuka Devi D. Sivaraj T. Tamizh Chelvam |
| author_facet | V. Renuka Devi D. Sivaraj T. Tamizh Chelvam |
| author_sort | V. Renuka Devi |
| collection | DOAJ |
| description | ℐ-open sets were introduced and studied by Janković and Hamlett (1990) to generalize the well-known Banach category theorem. Quasi-ℐ-openness was introduced and studied by Abd El-Monsef et al. (2000). These are ∗-dense-in-itself sets of the ideal spaces. In this note, properties of these sets are further investigated and characterizations of these sets are given. Also, their relation with ℐ-dense sets and ℐ-locally closed sets is discussed. Characterizations of completely codense ideals are given in terms of semi-preopen sets. |
| format | Article |
| id | doaj-art-7de3bccb5d5e4e1a822ff6efb0e42130 |
| institution | Kabale University |
| issn | 0161-1712 1687-0425 |
| language | English |
| publishDate | 2004-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | International Journal of Mathematics and Mathematical Sciences |
| spelling | doaj-art-7de3bccb5d5e4e1a822ff6efb0e421302025-02-03T05:52:19ZengWileyInternational Journal of Mathematics and Mathematical Sciences0161-17121687-04252004-01-012004723989399910.1155/S0161171204403391Properties of some ∗-dense-in-itself subsetsV. Renuka Devi0D. Sivaraj1T. Tamizh Chelvam2Department of Mathematics, Govindammal Aditanar College for Women, Tiruchendur 628 215, Tamil Nadu, IndiaDepartment of Mathematics, Aditanar College of Arts and Science, Tiruchendur 628216, Tamil Nadu, IndiaDepartment of Mathematics, Manonmaniam Sundaranar University, Tirunelveli 627 012, Tamil Nadu, Indiaℐ-open sets were introduced and studied by Janković and Hamlett (1990) to generalize the well-known Banach category theorem. Quasi-ℐ-openness was introduced and studied by Abd El-Monsef et al. (2000). These are ∗-dense-in-itself sets of the ideal spaces. In this note, properties of these sets are further investigated and characterizations of these sets are given. Also, their relation with ℐ-dense sets and ℐ-locally closed sets is discussed. Characterizations of completely codense ideals are given in terms of semi-preopen sets.http://dx.doi.org/10.1155/S0161171204403391 |
| spellingShingle | V. Renuka Devi D. Sivaraj T. Tamizh Chelvam Properties of some ∗-dense-in-itself subsets International Journal of Mathematics and Mathematical Sciences |
| title | Properties of some ∗-dense-in-itself subsets |
| title_full | Properties of some ∗-dense-in-itself subsets |
| title_fullStr | Properties of some ∗-dense-in-itself subsets |
| title_full_unstemmed | Properties of some ∗-dense-in-itself subsets |
| title_short | Properties of some ∗-dense-in-itself subsets |
| title_sort | properties of some ∗ dense in itself subsets |
| url | http://dx.doi.org/10.1155/S0161171204403391 |
| work_keys_str_mv | AT vrenukadevi propertiesofsomedenseinitselfsubsets AT dsivaraj propertiesofsomedenseinitselfsubsets AT ttamizhchelvam propertiesofsomedenseinitselfsubsets |